Packet transport and load distribution in scale-free network models

In scale-free networks, the degree distribution follows a power law with the exponent γ. Many model networks exist which reproduce the scale-free nature of the real-world networks. In most of these models, the value of γ is continuously tunable, thus is not universal. We study a problem of data packet transport in scale-free networks and define load at each vertex as the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest paths. We find that the load distribution follows a power law with an exponent δ for scale-free networks. Moreover, the load exponent δ is insensitive to the details of the networks in the range 2<γ⩽3. For the class of networks considered in this work, δ≈2.2(1). We conjecture that the load exponent is a universal quantity to characterize and classify scale-free networks.